Universal adaptive torque control for pm motors for field-weakening region operation

ABSTRACT

The invention includes a motor controller and method for controlling a permanent magnet motor. In accordance with one aspect of the present technique, a permanent magnet motor is controlled by, among other things, receiving a torque command, determining a normalized torque command by normalizing the torque command to a characteristic current of the motor, determining a normalized maximum available voltage, determining an inductance ratio of the motor, and determining a direct-axis current based upon the normalized torque command, the normalized maximum available voltage, and the inductance ratio of the motor.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH & DEVELOPMENT

This invention was made with Government support under contract numberNREL-ZCL-3-32060-03; W(A)-03-011, CH-1137 awarded by Department ofEnergy. The Government has certain rights in the invention.

BACKGROUND

The invention relates generally to torque control of a permanent magnetmotor. More particularly, the invention relates to a technique fortorque control of a permanent magnet motor operating above base speed.

Three phase interior permanent magnet synchronous motors (IPMSM) receivethree phases of electrical voltage, which enter three stator windings ofthe motor to produce a rotating magnetic stator field. The rotatingmagnetic stator field interacts with a magnetic field associated withthe permanent magnets of the motor. The rotor rotates based oninteractions between the magnetic stator field and the permanentmagnetic field of the rotor.

To more precisely control the output torque and speed of the motor, asynchronous reference frame may be employed, which is represented by aquadrature axis (q) and a direct axis (d) defined by the relativelocation of the rotor to the stator windings. In the synchronousreference frame, voltages for obtaining a particular torque and speedmay be more easily determined. Once direct-axis and quadrature-axisvoltages are obtained for the motor in the synchronous reference frame,a mathematical transformation may be used to produce the equivalentthree-phase voltage in a stationary reference frame, in which (a), (b),and (c) axes are defined by the location of the stator windings of themotor. The three-phase voltage in the stationary reference frame maysubsequently be used to drive the motor.

When operating below base speed (generally considered to be a speed atwhich a voltage limit has been reached and additional speed may beachieved primarily by weakening the magnetic fields of permanent magnetsin the rotor), the amount of torque output by the motor may generally beadjusted by changing the magnitude and frequency of the driving voltagesin a relatively straightforward manner. To operate above base speed, thestator current in the direct axis of the permanent magnet motor operatesto weaken the magnetic field of the permanent magnets, and thus a motoroperating above base speed may be referred to be operating in afield-weakening region. However, as the magnetic field of the permanentmagnets is reduced, control becomes much more complex. Though techniquesfor generating a maximum torque per amperes with a permanent magnetmotor have been developed, the techniques remain limited to veryspecific applications and may vary considerably from one motor toanother.

BRIEF DESCRIPTION

The invention includes a motor controller and technique for controllinga permanent magnet motor. In accordance with one aspect of the presenttechnique, a permanent magnet motor is controlled by, among otherthings, receiving a torque command, determining a normalized torquecommand by normalizing the torque command to a characteristic current ofthe motor, determining a normalized maximum available voltage,determining an inductance ratio of the motor, and determining adirect-axis current based upon the normalized torque command, thenormalized maximum available voltage, and the inductance ratio of themotor. Determining the normalized maximum available voltage may includedividing a rated voltage over a total of a stator frequency multipliedby a flux of permanent magnets of the motor. Determining the inductanceratio of the motor may include determining a value equal to aquadrature-axis inductance divided over a direct-axis inductance, fromwhich a value of 1 is subtracted. The direct-axis current may bedetermined by, for example, using a numerical method or a closed loopsolver method to obtain a normalized direct-axis current. Determiningthe normalized direct-axis current using a numerical method may includeusing a precalculated table with solutions based upon the normalizedtorque command, the normalized maximum available voltage, and theinductance ratio of the motor.

In accordance with another aspect of the invention, a motor controllermay include, among other things, an inverter configured to supply athree-phase voltage to a permanent magnet motor, driver circuitryconfigured to cause the inverter to supply the three-phase voltage tothe permanent magnet motor based on a control signal, and controlcircuitry configured to receive a torque command and generate thecontrol signal based at least in part on a value of a normalizeddirect-axis current, wherein the control circuitry is configured todetermine the value of the normalized direct-axis current based on thetorque command, a stator frequency, a rated voltage of the motor, acharacteristic current of the motor, a permanent magnet flux of themotor, and an inductance ratio of the motor. The control circuitry maybe configured to determine the value of the normalized direct-axiscurrent, such as via a numerical method or a closed-loop solver. Forexample, the control circuitry may determine the value the normalizeddirect-axis current using a using a precalculated table with solutionsbased upon a normalized torque command, a normalized maximum availablevoltage, and the inductance ratio of the motor.

In accordance with another aspect of the invention, a table for use incontrolling a permanent magnet motor in above base speed operationincludes a plurality of normalized values for optimum direct-axiscurrent, wherein each of the plurality of normalized values for optimumdirect-axis current corresponds to a value for optimum direct-axiscurrent in a given permanent magnet motor when multiplied by acharacteristic current of the given permanent magnet motor. In thetable, the plurality of normalized values for optimum direct-axiscurrent may relate to a motor inductance ratio, a normalized torquecommand, and a maximum available voltage.

DRAWINGS

These and other features, aspects, and advantages of the presentinvention will become better understood when the following detaileddescription is read with reference to the accompanying drawings in whichlike characters represent like parts throughout the drawings, wherein:

FIG. 1 is a simplified diagram of an interior permanent magnetsynchronous motor;

FIG. 2 is a dynamic block diagram of the interior permanent magnetsynchronous motor of FIG. 1 in a synchronous reference frame;

FIG. 3 is a vector diagram representing the phasors of operatingparameters of the interior permanent magnet synchronous motor of FIG. 1;

FIG. 4 is a block diagram of a torque limit control of the interiorpermanent magnet synchronous motor of FIG. 1 for above base speedoperation in accordance with an aspect of the invention;

FIG. 5 is a block diagram of an optimum torque control of the interiorpermanent magnet synchronous motor of FIG. 1 for above base speedoperation employing a three-dimensional table in accordance with anaspect of the invention;

FIG. 6 represents an exemplary two-dimensional component of athree-dimensional table for application in the optimum torque controlblock diagram depicted in FIG. 5; and

FIG. 7 is a block diagram of an optimum torque control of the interiorpermanent magnet synchronous motor of FIG. 1 for above base speedoperation employing a closed-loop solver in accordance with an aspect ofthe invention.

DETAILED DESCRIPTION

FIG. 1 is a simplified diagram of an interior permanent magnetsynchronous motor 10. The motor 10 includes conductive material 12(typically ferromagnetic) and permanent magnets 14. Three statorwindings 16, 18, and 20 receive a three-phase current to produce astator magnetic field. The stator magnetic field interacts with amagnetic field caused by permanent magnets 14 within a rotor 22, causingthe rotor 22 to rotate accordingly.

Three-phase voltage may generally be supplied to the stator windings 16,18, and 20 by way of an inverter module (not shown), which may receivepower from a DC voltage supply. Driver circuitry may direct the invertermodule to output the three-phase power at a desired frequency, basedupon control signals received by the driver circuitry from controlcircuitry. The control circuitry may generally determine the appropriatecontrol signals to send to the driver circuitry based upon a torquesignal received from an operator or remote controller, as well asfeedback from the motor 10, the inverter module, the driver circuitry,and from calculations carried out within the control circuitry. Toperform motor control operations, the control circuitry may include anappropriate processor, such as a microprocessor or field programmablegate array, and may perform a variety of motor control calculations,including those techniques described herein. The control circuitry mayinclude a memory device or a machine-readable medium such as Flashmemory, EEPROM, ROM, CD-ROM or other optical data storage media, or anyother appropriate storage medium which may store data or instructionsfor carrying out the foregoing techniques.

To simplify the analysis of the motor 10, it may be assumed thatmaterial 12 has a permeability equal to infinity (i.e., there is nosaturation), that the stator windings are assumed to be sinusoidaldistributed (i.e., magneto motive force (mmf) space harmonics and slotharmonics may be neglected), and that the stator winding fields areassumed to be sinusoidally distributed, (i.e., only the first harmonicis shown). Additionally, the stator windings may be assumed to besymmetric, and thus winding turns, resistance, and inductances may beassumed to be equal. Further, a lumped-parameter circuit model may alsobe assumed.

In a stationary reference frame, the voltage and torque associated withstator windings 16, 18, and 20 of motor 10 may be represented by thefollowing equations, where x represents the phases a, b, or c of motor10:

$\begin{matrix}{{V_{x} = {{R \cdot i_{x}} + \frac{\psi_{x}}{t}}};} & (1) \\{{\Sigma \; T} = {J \cdot {\frac{\omega}{t}.}}} & (2)\end{matrix}$

In equation (1), V_(x) represents the instantaneous phase voltage [V], Rrepresents the stator phase resistance [Ω], i_(x) represents theinstantaneous stator phase current [A], and Ψ_(x) represents theinstantaneous stator flux linkage [Wb]. In equation (2), ΣT represents asum of all torque [Nm], including load torque, of the motor 10, Jrepresents the moment of inertia [kg m²], and o represents rotor speed[rad/sec].

Flux linkage Ψ_(a), Ψ_(b), and Ψ_(c) for stator windings 16, 18, and 20of motor 10 may be described according to the following equations:

$\begin{matrix}{\left. \begin{matrix}{\psi_{a} = {{L_{a} \cdot i_{a}} + {L_{ab} \cdot i_{b}} + {L_{ac} \cdot i_{c}} + \psi_{am}}} \\{\psi_{b} = {{L_{ba} \cdot i_{a}} + {L_{b} \cdot i_{b}} + {L_{bc} \cdot i_{c}} + \psi_{bm}}} \\{\psi_{c} = {{L_{ca} \cdot i_{a}} + {L_{cb} \cdot i_{b}} + {L_{c} \cdot i_{c}} + \psi_{cm}}}\end{matrix} \right\}.} & (3)\end{matrix}$

In equation (3) above, L_(a), L_(b), and L_(c) represent self-inductance[H], L_(ab), L_(ba), L_(ac), L_(ca), L_(bc), and L_(cb) represent mutualinductances [H], and Ψ_(am), Ψ_(bm, and Ψ) _(cm) represent flux linkage[Wb] from the permanent magnets 14, The values of self inductance andmutual inductance are a function of the rotor 22 position, which vary asthe rotor 22 rotates relative to the stator windings a 16, b 18, and c20. Mutual-inductances L_(ab), L_(ba), L_(ac), L_(ca), L_(bc), andL_(cb) also conform to the following equations:

$\begin{matrix}{\left. \begin{matrix}{L_{ab} = L_{ba}} \\{L_{ac} = L_{ca}} \\{L_{bc} = L_{cb}}\end{matrix} \right\}.} & (4)\end{matrix}$

Continuing to view FIG. 1, motor 10 may be understood to operate in asynchronous reference frame as well as a stationary frame. Thesynchronous reference frame includes a quadrature axis (q) 24 and adirect axis (d) 26. The quadrature axis (q) 24 is defined by therelative location of the permanent magnets of the rotor 22, and directaxis (d) 26 is defined relative to an angular position γ_(e) 28 fromstator windings a 16, b 18, and c 20. The equations for the motor 10 inthe synchronous reference frame may be written in the following form:

$\begin{matrix}{{V_{d} = {{R \cdot I_{d}} + {L_{d} \cdot \frac{I_{d}}{t}} - {L_{q} \cdot I_{q} \cdot \frac{\gamma_{e}}{t}}}};} & (5) \\{{V_{q} = {{R \cdot I_{q}} + {L_{q} \cdot \frac{I_{q}}{t}} + {\left( {{L_{d} \cdot I_{d}} + \psi_{m\; 0}} \right) \cdot \frac{\gamma_{e}}{t}}}};} & (6) \\{{J \cdot \frac{^{2}\gamma_{e}}{t^{2}}} = {{\frac{3}{2} \cdot p_{n} \cdot \left\lbrack {{\Psi_{m\; 0} \cdot I_{q}} + {\left( {L_{d} - L_{q}} \right) \cdot I_{d} \cdot I_{q}}} \right\rbrack} - {T_{load}.}}} & (7)\end{matrix}$

The equations above describe motor 10 in the synchronous reference frame(d, q). As such, V_(d) represents a direct-axis voltage [V] and V_(q)represents a quadrature-axis voltage [V] applied to the motor 10, Rrepresents the stator resistance [Ω], I_(d) represents a flux-producingcurrent [A] and I_(q) represents a torque-producing current [A], L_(d)and L_(q) represent direct-axis and quadrature-axis inductances [H],respectively, γ_(e) represents angular distance γ_(e) 28 [rad/sec],Ψ_(m0) represents the magnetic flux [Wb] of the pole pairs of the rotor22, p_(n) represents the number of permanent magnets of the rotor 22,and T_(load) represents the torque [Nm] exerted against motor 10 by theload. Self inductance L_(d) and L_(q) may be further representedaccording to equations (8) and (9) below. It should be noted thatusually for a surface permanent magnet synchronous motor, L_(d) is equalto L_(q).

$\begin{matrix}{{L_{d} = {{\frac{3}{2} \cdot \left( {L_{0} + L_{m}} \right)} = {\frac{3}{2} \cdot L_{d \cdot {ph}}}}};} & (8) \\{L_{q} = {{\frac{3}{2} \cdot \left( {L_{0} + L_{m}} \right)} = {\frac{3}{2} \cdot {L_{q \cdot {ph}}.}}}} & (9)\end{matrix}$

Turning to FIG. 2, a dynamic block diagram 30 represents the interiorpermanent magnet synchronous motor 10 in a synchronous reference frame(d, q). With known values of the three-phase voltage waveforms 32 andthe relative angular position γ_(e) 34, a coordinate transformation 36may be performed, producing direct-axis voltage V_(d) 38, andquadrature-axis voltage V_(q) 40. In accordance with equation (5) above,a summer 42 adds direct-axis voltage V_(d) 38, subtracts direct-axiscurrent I_(d) 44 multiplied by stator resistance R 46, and adds voltageE_(d) 48, outputting direct-axis change in flux

${\frac{\Psi_{d}}{t}\mspace{14mu} 50},$

which is equal to

$L_{d} \cdot {\frac{I_{d}}{t}.}$

The origin of voltage E_(d) 48 will be discussed further below.

Because direct-axis change in flux

$\frac{\Psi_{d}}{t}\mspace{14mu} 50$

is equal to

${L_{d} \cdot \frac{I_{d}}{t}},$

multiplying the inverse of direct-axis inductance

$\frac{1}{L_{d}}\mspace{14mu} 52$

by direct-axis change in flux

$\frac{\Psi_{d}}{t}\mspace{14mu} 50$

produces direct-axis change in current

$\frac{I_{d}}{t}\mspace{14mu} 54.$

When direct-axis change is in current

$\frac{I_{d}}{t}\mspace{14mu} 54$

is integrated by the Laplace operator

${\frac{1}{s}\mspace{14mu} 56},$

direct-axis current I_(d) 44 results.

By multiplying direct-axis current I_(d) 44 with direct-axis inductanceL_(d) 58, direct-axis flux Ψ_(d) 60 is produced. Direct-axis flux Ψ_(d)60 may subsequently enter multiplier 62 with stator frequency ω_(e) 64,producing voltage L_(d)L_(d)ω_(e) 66. Permanent magnet flux Ψ_(m0) 68and stator frequency ω_(e) 70 multiplied in multiplier 72 producevoltage E₀ 74. When voltage L_(d)I_(d)ω_(e) 66 is added to voltage E₀ 74in summer 76, voltage E_(q) 78 results.

As apparent from equation (6), when summer 80 subtracts voltage E_(q) 78from quadrature-axis voltage V_(q) 40 and quadrature-axis current I_(q)82 multiplied by stator resistance R 84, the result is quadrature-axischange in flux

${\frac{\Psi_{q}}{t}\mspace{14mu} 86},$

which is equal to

$L_{q} \cdot {\frac{I_{q}}{t}.}$

Multiplying by the inverse of quadrature-axis inductance

$\frac{1}{L_{q}}88$

thus produces quadrature-axis change in current

${\frac{I_{q}}{t}\mspace{14mu} 90},$

which may be integrated via the Laplace operator 1/s 92 to produce thequadrature-axis current I_(q) 82.

When quadrature-axis current I_(q) 82 is multiplied by quadrature-axisinductance L_(q) 94, the result is quadrature-axis flux Ψ_(q) 96.Multiplying quadrature-axis flux Ψ_(q) 96 and stator frequency ω_(e) 64in multiplier 98 produces voltage E_(d) 48, which enters summer 42, asdiscussed above.

Quadrature-axis current I_(q) 82 enters multiplier 100 where it ismultiplied by direct-axis current I_(d) 44. The result is multiplied byblock 102, which represents a value of the direct-axis inductance L_(d)less the quadrature-axis inductance L_(q), and subsequently enterssummer 104. Meanwhile, permanent magnet flux Ψ_(m0) 68 is multiplied byquadrature-axis current I_(q) 82 in multiplier 106 which enters summer104. The output of summer 104 is subsequently multiplied by block 108,which represents the value

${\frac{3}{2} \cdot P_{n}},$

to produce a motor torque T_(mot) 110 representing the torque output bymotor 10.

The load torque T_(load) 112 may be subtracted from motor torque T_(mot)110 in summer 114, producing an excess torque

$J\frac{^{2}\gamma_{e}}{t^{2}}\mspace{14mu} 116.$

In block 118,

$\frac{1}{J \cdot s},$

the moment of inertia J is divided from excess torque

$J\frac{^{2}\gamma_{e}}{t^{2}}\mspace{14mu} 116$

and excess torque

$J\frac{^{2}\gamma_{e}}{t^{2}}\mspace{14mu} 116$

is integrated, resulting in motor frequency ω 120 of motor 10.

By multiplying motor frequency ω 120 by permanent magnet pole pairsp_(n), stator frequency ω_(e) 64 and 70 may be obtained. Motor frequencyω 120 may also be integrated in Laplace integral 1/s 122 to produce amotor angular position γ 124. The motor angular position γ 124 may besubsequently multiplied by permanent magnet pole pairs p_(n) 126 toobtain angular position γ₃₄.

As illustrated by dynamic block diagram 30, equations (5) and (6) may berewritten for a steady state condition, according to the followingequations:

V _(d) =R·I _(d) −L _(q) ·I _(q)ω_(e)   (10);

V _(q) =R·I _(q) +ω _(e) ·L _(d) L _(d)+ω_(m0)   (11).

Equations (10) and (11) may alternatively be expressed in the followingform:

V _(d) =R·I _(d) −E _(d)   (12);

V _(q) =R·I _(q) +E _(q)   (13).

In equations (12) and (13), E_(d) and E_(q) may be defined according tothe following equations:

$\begin{matrix}{{E_{d} = {L_{q} \cdot I_{q} \cdot \omega_{e}}};} & (14) \\\begin{matrix}{E_{q} = {{L_{d} \cdot I_{d} \cdot \omega_{e}} + {\Psi_{m\; 0} \cdot \omega_{e}}}} \\{{= {{L_{d} \cdot I_{d} \cdot \omega_{e}} + E_{0}}};}\end{matrix} & (15) \\\begin{matrix}{E_{\Sigma} = \sqrt{E_{d}^{2} + E_{q}^{2}}} \\{= {\omega_{e} \cdot {\sqrt{\left( {L_{q} \cdot I_{q}} \right)^{2} + \left( {{L_{d} \cdot I_{d}} + \Psi_{m\; 0}} \right)^{2}}.}}}\end{matrix} & (16)\end{matrix}$

FIG. 3 represents a basic vector diagram 128 of the motor 10, based uponequations (10)-(16) above. A stator current I_(st) 130 may be brokeninto direct-axis and quadrature-axis components, direct-axis currentI_(d) 132 and quadrature-axis current I_(q) 134, based upon on themagnitude of stator current I_(st) 130 and an angle β 136. A statorvoltage V_(a) 138 may be broken into direct-axis and quadrature-axiscomponents direct-axis voltage V_(d) 140 and quadrature-axis voltageV_(q) 142.

Direct-axis voltage V_(d) 140 may be further broken into a voltage E_(d)144 component less a voltage drop I_(d)·R 146, representing the voltagedrop across stator resistance R caused by direct-axis current I_(d).

Quadrature-axis voltage V_(q) 142 may also be broken into additionalcomponents. Voltage E_(q) 148 is equal to voltage E₀ 150, whichrepresents a value of stator frequency ω_(e) multiplied by permanentmagnet flux ω_(m0), less a voltage ω_(e)L_(d)·I_(d) 152. Quadrature-axisvoltage V_(q) 142 may be obtained by adding voltage drop I_(q)·R 154,representing a voltage drop across stator resistance R caused byquadrature-axis current I_(q), to voltage E_(q) 148.

Flux 156 may be broken into direct-axis and quadrature-axis components,direct-axis flux ω_(d) 158 and quadrature-axis flux ω_(q) 160. To obtainflux 156, vectors representing permanent magnet flux ω_(m0) 162,quadrature-axis flux ω_(q) 160, and flux L_(d)·I_(d) 164 may be summed.

To obtain an optimum torque control algorithm for above base speedoperation, a torque equation should be considered. A general equationrepresenting motor torque T_(mot) in the synchronous reference frame maybe written as follows:

$\begin{matrix}{T_{mot} = {\frac{3}{2} \cdot p_{n} \cdot I_{q} \cdot {\left\lbrack {\Psi_{m\; 0} - {\left( {L_{q} - L_{d}} \right) \cdot I_{d}}} \right\rbrack.}}} & (17)\end{matrix}$

By rewriting equations (10) and (11) with the assumption that thevoltage drop across stator resistance R is negligible above base speed,the following equations may be obtained:

V _(d)=−ω_(e) ·L _(q) ·I _(q)   (18);

V _(q) =ω _(e) ·L _(d) ·I _(d)ω_(e)Ψ_(m0)   (19)

When motor 10 operates above base speed, motor voltage remains constantaccording to the following equation:

V _(d·rtd) ² +V _(q·rtd) ² =V _(rtd) ²   (20).

To achieve above base speed operation, direct-axis current I_(d) maycause permanent magnets 14 of motor 10 to become temporarily weakened ordemagnetized. A direct-axis current I_(d) that fully demagnetizes thepermanent magnets 14 may be referred to as the “characteristic current.”The characteristic current I_(df) may be represented by the followingequation:

$\begin{matrix}{I_{df} = {- {\frac{\Psi_{m\; 0}}{L_{d}}.}}} & (21)\end{matrix}$

The torque equation may be normalized to the characteristic currentI_(df). Accordingly, a normalized torque is defined according to thefollowing equations:

$\begin{matrix}\begin{matrix}{\hat{T} = \frac{T_{mot}}{T_{base}}} \\{= {\frac{T_{mot}}{\frac{3}{2} \cdot p_{n} \cdot \Psi_{m\; 0} \cdot I_{df}}.}}\end{matrix} & (22)\end{matrix}$

In the above equation (22), normalized base torque T_(base) is definedaccording to the following equation:

$\begin{matrix}{T_{base} = {\frac{3}{2} \cdot p_{n} \cdot \Psi_{m\; 0} \cdot {I_{df}.}}} & (23)\end{matrix}$

Substituting equation (17) into equation (22) produces the followingequation:

$\begin{matrix}\begin{matrix}{\hat{T} = {\frac{I_{q}}{I_{df}} \cdot \left\lbrack {1 - \frac{L_{d} \cdot \left( {\frac{L_{q}}{L_{d}} - 1} \right) \cdot I_{d}}{\Psi_{m\; 0}}} \right\rbrack}} \\{= {\frac{I_{q}}{I_{df}} \cdot \left\lbrack {1 - \frac{\left( {\frac{L_{q}}{L_{d}} - 1} \right) \cdot I_{d}}{\frac{\Psi_{m\; 0}}{L_{d}}}} \right\rbrack}} \\{= {\frac{I_{q}}{I_{df}} \cdot {\left\lbrack {1 - {\left( {\frac{L_{q}}{L_{d}} - 1} \right) \cdot \frac{I_{d}}{I_{df}}}} \right\rbrack.}}}\end{matrix} & (24)\end{matrix}$

Thus, the following normalized torque equation may be rewritten as thefollowing equation:

{circumflex over (T)}=Î _(q)·(1−K·Î _(d))   (25).

Equations (18) and (19) may also be rewritten in a normalized, per-unitform, according to the following equations:

$\begin{matrix}{\begin{matrix}{\frac{V_{d}}{\omega_{e\; 0} \cdot \Psi_{m\; 0}} = {\hat{V}}_{d}} \\{= \frac{{- \omega_{e}} \cdot L_{q} \cdot I_{q} \cdot L_{d}}{\omega_{e\; 0} \cdot \Psi_{m\; 0} \cdot L_{d}}} \\{= {{- {\hat{\omega}}_{e}} \cdot \left( {K + 1} \right) \cdot {\hat{I}}_{q}}}\end{matrix}{or}{\frac{{\hat{V}}_{d}}{{\hat{\omega}}_{e}} = {{- \left( {K + 1} \right)} \cdot {{\hat{I}}_{q}.}}}} & (26) \\{\begin{matrix}{\frac{V_{q}}{\omega_{e\; 0} \cdot \Psi_{m\; 0}} = {\hat{V}}_{q}} \\{= {\frac{\omega_{e} \cdot L_{d} \cdot I_{d}}{\omega_{e\; 0} \cdot \Psi_{m\; 0}} + \frac{\omega_{e\; 0} \cdot \Psi_{m\; 0}}{\omega_{e\; 0} \cdot \Psi_{m\; 0}}}} \\{= {{\hat{\omega}}_{e} \cdot \left( {{\hat{I}}_{d} + 1} \right)}}\end{matrix}{or}{\frac{{\hat{V}}_{d}}{{\hat{\omega}}_{e}} = {\left( {{\hat{I}}_{d} + 1} \right).}}} & (27)\end{matrix}$

The motor voltage in a normalized form may thus be written as follows:

$\begin{matrix}\begin{matrix}{\frac{{\hat{V}}_{d \cdot {rtd}}^{2} + {\hat{V}}_{q \cdot {rtd}}^{2}}{{\hat{\omega}}_{e}^{2}} = \frac{{\hat{V}}_{rtd}^{2}}{{\hat{\omega}}_{e}^{2}}} \\{= {\hat{V}}_{\max}^{2}} \\{= {{{\hat{I}}_{q}^{2} \cdot \left( {K + 1} \right)^{2}} + {\left( {{\hat{I}}_{d} + 1} \right)^{2}.}}}\end{matrix} & (28)\end{matrix}$

In equation (28) above, normalized quadrature-axis current Î_(q),normalized direct-axis current Î_(d), normalized stator frequency{circumflex over (ω)}_(e), normalized maximum available voltage{circumflex over (V)}_(max), and motor inductance ratio K may bedescribed according to the following equations:

$\begin{matrix}{\left. \begin{matrix}{{{\hat{I}}_{q} = \frac{I_{q}}{I_{df}}};} \\{{{\hat{I}}_{q} = \frac{I_{q}}{I_{df}}};} \\{{{\hat{\omega}}_{e} = \frac{\omega_{e}}{\omega_{e\; 0}}};} \\{{{\hat{V}}_{\max} = {\frac{{\hat{V}}_{rtd}}{{\hat{\omega}}_{e}} = {\frac{V_{rtd} \cdot \omega_{e\; 0}}{\omega_{e\; 0} \cdot \Psi_{m\; 0} \cdot \omega_{e}} = \frac{V_{rtd}}{\Psi_{m\; 0} \cdot \omega_{e}}}}};} \\{K = \left( {\frac{L_{q}}{L_{d}} - 1} \right)}\end{matrix} \right\}.} & (29)\end{matrix}$

From the equations above, two normalized equations sharing two unknownvariables normalized direct-axis current Î_(d) and normalizedquadrature-axis current Î_(q), an above base speed operation may bedetermined. Normalized torque {circumflex over (T)} and normalizedmaximum available voltage {circumflex over (V)}_(max) may be obtained byway of the following equations:

{circumflex over (T)}=Î _(q)·(1−K·Î _(d)   (30);

{circumflex over (V)} _(max) ² =Î _(q) ²·(K+1)²+(Î _(d)+1)²   (31).

From equations (30) and (31), normalized torque {circumflex over (T)}may be reduced to a function of normalized direct-axis current Î_(d),normalized maximum available voltage {circumflex over (V)}_(max), andmotor inductance ratio K, in accordance with the following equation:

{circumflex over (T)} ²·(K+1)²=(1−K·Î _(d))² ·└{circumflex over (V)}_(max) ²−(1+Î _(d))²┘  (32).

Equation (32) may be rewritten according to the following equation:

$\begin{matrix}{\hat{T} = {\frac{1 - {K \cdot {\hat{I}}_{d}}}{K + 1} \cdot {\sqrt{{\hat{V}}_{m\; {ax}}^{2} - \left( {1 + {\hat{I}}_{d}} \right)^{2}}.}}} & (33)\end{matrix}$

From equations (32) or (33), a theoretical maximum torque value may bedetermined as a function of normalized direct-axis current Î_(d). Alocal maximum of normalized torque {circumflex over (T)} may be obtainedwith a derivative according to the following equation:

$\begin{matrix}\begin{matrix}{\frac{\hat{T}}{{\hat{I}}_{d}} = {{{- \frac{K}{K + 1}} \cdot \cdot \sqrt{{\hat{V}}_{m\; {ax}}^{2} - \left( {1 + {\hat{I}}_{d}} \right)^{2}}} -}} \\{\frac{\left( {1 - {K \cdot {\hat{I}}_{d}}} \right)\left( {1 + {\hat{I}}_{d}} \right)}{\left( {K + 1} \right) \cdot \sqrt{{\hat{V}}_{m\; {ax}}^{2} - \left( {1 + {\hat{I}}_{d}} \right)^{2}}}} \\{= 0.}\end{matrix} & (34)\end{matrix}$

Equation (34) may alternatively be rewritten as the following equation:

$\begin{matrix}{{{{- K} \cdot \left\lbrack {{\hat{V}}_{m\; {ax}}^{2} - \left( {1 + {\hat{I}}_{d\_ \max}} \right)^{2}} \right\rbrack} - {\left( {1 - {K \cdot {\hat{I}}_{d\_ \max}}} \right) \cdot \left( {1 + {\hat{I}}_{d\_ \max}} \right)}} = 0.} & (35)\end{matrix}$

By manipulating equation (35), the following equation may be derived:

$\begin{matrix}{{{\hat{I}}_{d\_ \max}^{2} + {\frac{{3 \cdot K} - 1}{2 \cdot K} \cdot I_{d\_ \max}} - {\frac{1}{2} \cdot \left( {\frac{1}{K} + V_{m\; {ax}}^{2} - 1} \right)}} = 0.} & (36)\end{matrix}$

It will be apparent that equation (36) is a quadratic equation innormalized direct-axis current Î_(d). When motor inductance ratio K isgreater than zero, meaning that the permanent magnets 14 of motor 10 arelocated beneath the surface of the rotor 22, the solution of theequation is equal to the following equation:

$\begin{matrix}{{\hat{I}}_{{d\_ \max}{({K > 0})}} = {\frac{1 - {3 \cdot K} - \sqrt{{K^{2} \cdot \left( {{8 \cdot {\hat{V}}_{m\; {ax}}^{2}} + 1} \right)} + {2 \cdot K} + 1}}{4 \cdot K}.}} & (37)\end{matrix}$

When motor inductance ratio K is equal to zero, meaning that thepermanent magnets 14 of motor 10 are located on the surface of the rotor22, the following equations may be obtained:

$\begin{matrix}{{\hat{T} = \sqrt{{\hat{V}}_{{ma}\; x}^{2} - \left( {1 + {\hat{I}}_{d}} \right)^{2}}};} & (38) \\{\frac{\hat{T}}{{\hat{I}}_{d{({K = 0})}}} = {{- \frac{\left( {1 + {\hat{I}}_{d}} \right)}{\sqrt{{\hat{V}}_{m\; {ax}}^{2} - \left( {1 + {\hat{I}}_{d}} \right)^{2}}}} = 0.}} & (39)\end{matrix}$

As a result, when motor inductance ratio K is equal to zero, thenormalized maximum direct-axis current Î_(d) _(—) _(max(K=0)) is equalto negative 1, as illustrated in the following equation:

Î _(d) _(—) _(max(K=0))=−1   (40).

A normalized maximum torque may be found by substituting the maximumdirect access current Î_(dmax) into equation (34). As a result, thenormalized maximum torque {circumflex over (T)}_(max(K>0)) when motorinductance ratio K is greater than zero will be equal to the followingequation:

$\begin{matrix}{{\hat{T}}_{m\; {{ax}{({K > 0})}}} = {\frac{\left( {10{K \cdot {\hat{I}}_{d\_ \max}}} \right)}{K + 1} \cdot {\sqrt{{\hat{V}}_{m\; {ax}}^{2} - \left( {1 + {\hat{I}}_{d\_ \max}} \right)^{2}}.}}} & (41)\end{matrix}$

Accordingly, the normalized maximum torque {circumflex over(T)}_(max(K=0)) when motor inductance ratio K is equal to zero may bedescribed according to the equation (40) and (41) below:

{circumflex over (T)} _(max(K=0)) ={circumflex over (V)} _(max)   (42).

Turning to FIG. 4, a torque limit control block diagram 166 for abovebase speed operation of motor 10 illustrates a manner of appropriatelylimiting a reference torque command T_(ref) 168 to produce a normalizedtorque command {circumflex over (T)}_(command) _(—) _(pu) 170. Thenormalized torque command {circumflex over (T)}_(command) _(—) _(pu) 170is limited to prevent motor control circuitry and driver circuitry fromattempting to exact a torque from motor 10 that would be impossible orthat could result in a loss of control of motor 10.

To obtain the normalized torque command {circumflex over (T)}_(command)_(—) _(pu) 170, the reference torque command T_(ref) 168 may first benormalized by multiplying the reference torque command T_(ref) 168 bythe contents of block 172, producing a normalized reference torque{circumflex over (T)}_(ref) _(—) _(pu) 174. The normalized referencetorque {circumflex over (T)}_(ref) _(—) _(pu) 174 subsequently enters atorque limiter 176. If the normalized referenced torque {circumflex over(T)}_(ref) _(—) _(pu) 174 exceeds a normalized torque limit {circumflexover (T)}_(Lim) 178, to be described in greater detail below, thenormalized torque command {circumflex over (T)}_(command) _(—) _(pu) 170is limited to, or made to equate, the normalized torque limit{circumflex over (T)}_(Lim) 178.

The normalized torque limit {circumflex over (T)}_(Lim) 178 represents achoice of the smallest 180 of either a normalized general torque limit{circumflex over (T)}_(Lim) _(—) _(general) _(—) _(pu) 182 or anormalized theoretical torque limit {circumflex over (T)}_(Lim) _(—)_(theoretical) _(—) _(pu) 184. To obtain a normalized general torquelimit {circumflex over (T)}_(Lim) _(—) _(general) _(—) _(pu) 182, ageneral torque limit T_(Lim) _(—) _(general) 186 is normalized throughmultiplication by the contents of block 188.

The torque limit control block diagram 166 may be broken down intosub-diagrams 190 and 192. Sub-diagram 190 represents a portion of thetorque limit control block diagram 166 that outputs the general torquelimit T_(Lim) _(—) _(general) 186, which represents a physical torquelimit above which the motor 10 may not physically produce additionaltorque.

To obtain the general torque limit T_(Lim) _(—) _(general) 186, a ratedstator frequency ω_(e·rtd) 194 is first divided in division block 196over a value representing an amount of stator frequency ω_(e) 198 which,in absolute value 200 terms, exceeds rated stator frequency ω_(e·rtd) byway of processing in block 202. A frequency ratio ω_(ratio) 204 results,which may be understood to represent a ratio of the rated statorfrequency ω_(e·rtd) 194 to the amount of stator frequency ω_(e) 198above base speed. The general torque limit T_(Lim) _(—) _(general) 186is produced by multiplying a torque overload ratio T_(overload) _(—)_(ratio) 206, a rated torque T_(rated) 208, and the frequency ratioω_(ratio) 204 in multiplier 210.

Continuing to view FIG. 4, sub-diagram 192 represents the portion oftorque limit control block diagram 166 that outputs the normalizedtheoretical torque limit {circumflex over (T)}_(Lim) _(—) _(theoretical)_(—) _(pu) 184, represents a theoretical torque limit above whichcontrol circuitry may lose some control of the motor 10. To obtain thenormalized theoretical torque limit {circumflex over (T)}_(Lim) _(—)_(theoretical) _(—) _(pu) 184, permanent magnet flux Ψ_(m0) 212 firstenters a multiplier 214 to be multiplied against a value representingthe amount of stator frequency ω_(e) 198 which, in absolute value 200terms, exceeds the rated stator frequency ω_(e·rtd) by way of processingin block 202. A voltage Ψ_(m0)·ω_(e) 216 results, which may also berepresented as voltage E₀.

Dividing a voltage V_(dc) 218 in division block 220 over √{square rootover (3)} 222 produces a numerator N 224 with a value equal to a ratedvoltage V_(rtd). Numerator N 224 is subsequently divided over voltageΨ_(m0)·ω_(e) 216 in division block 226, which in turn produces anormalized maximum available voltage {circumflex over (V)}_(max) 228.

If the value of block 230, which represents motor inductance ratio K232, is approximately greater than zero, as illustrated in block 234,then a normalized maximum direct-axis current Î_(d) _(—) _(max) 236should be calculated via equation block 238. Regardless as to the valueof motor inductance ratio K 232, normalized theoretical torque limit{circumflex over (T)}_(Lim) _(—) _(theoretical) _(—) _(pu) 184 isobtained by way of equation block 240, which accepts as inputs thenormalized maximum direct-axis current Î_(d) _(—) _(max) 236, motorinductance ratio K 232, and normalized maximum available voltage{circumflex over (V)}_(max) 228.

As discussed above, the smallest 180 value of either the normalizedgeneral torque limit {circumflex over (T)}_(Lim) _(—) _(general) _(—)_(pu) 182 or the normalized theoretical torque limit {circumflex over(T)}_(Lim) _(—) _(theoretical) _(—) _(pu) 184 subsequently representsthe normalized torque limit {circumflex over (T)}_(Lim) 178. After thereference torque command T_(ref) 168 is normalized in block 172,resulting in the normalized reference torque {circumflex over (T)}_(ref)_(—) _(pu) 174, the normalized reference torque {circumflex over(T)}_(ref) _(—) _(pu) 174 is limited to a maximum of the normalizedtorque limit {circumflex over (T)}_(Lim) 178 through torque limiter 176.The limited torque is ultimately output as the normalized torque command{circumflex over (T)}_(command) _(—) _(pu) 170.

A universal adaptive torque control algorithm which may provide maximumtorque per amperes control to a permanent magnet motor with any value ofinductance ratio K may also be obtained. To obtain a universal torquecontrol algorithm, normalized direct-axis current Î_(d) may be obtainedas a function of normalized torque {circumflex over (T)}, normalizedmaximum available voltage {circumflex over (V)}_(max), and motorinductance ratio K. From equations (30) and (31), the following fourthorder equation may be determined:

{circumflex over (T)} ²·(K+1)² ={circumflex over (V)} _(max) ²·(1−K·Î_(d))²−(1−K·Î _(d))²·(1+Î _(d))²   (43).

Equation (43) may not be easily solved analytically. Thus, a practicalimplementation may involve solving the above equations numerically orwith a closed loop solver. FIGS. 5-7 illustrate algorithms which mayprovide optimum torque control according to equation (43).

FIG. 5 illustrates an optimum torque control block diagram 242 employinga three-dimensional table to obtain a numerical solution of equation(43). In the three-dimensional table, values for normalized torque{circumflex over (T)}, normalized maximum available voltage {circumflexover (V)}_(max), and motor inductance ratio K serve as inputs, andnormalized direct-axis current Î_(d) is output. Since thethree-dimensional table employs calculations based on per-unit, ornormalized, variables, the table may be said to be universal. Beinguniversal, once the three-dimensional table is derived, the table mayapply to any permanent magnet motor, as the table accounts forcharacteristic current I_(df) and motor inductance ratio K.

The optimum torque control block diagram 242 begins when a referencetorque command T_(ref) 244 enters a torque limiter 246, which limits thereference torque command T_(ref) 244 to a torque limit T_(Lim) 248. Itshould be noted, however, the torque limiter 246 may also limit thereference torque command T_(ref) 244 using the method illustrated by thetorque limit control block diagram 166 of FIG. 4.

To obtain torque limit T_(Lim) 248, a rated stator frequency ω_(e·rtd)250 is divided in division block 252 over a value representing an amountof stator frequency ω_(e) 254 which, in terms of absolute value 256,exceeds rated stator frequency ω_(e·rtd) by way of processing in block258. A frequency ratio ω_(ratio) 260 results, which may be understood torepresent a ratio of the rated stator frequency ω_(e·rtd) 250 to theamount of stator frequency ω_(e) 254 above base speed. The torque limitT_(Lim) 248 is obtained by multiplying a maximum torque limitT_(Lim·Max) 262 in multiplier 264 by frequency ratio ω_(ratio) 260.

By multiplying the output of torque limiter 246 with the contents ofblock 266, a normalized reference torque {circumflex over (T)}_(ref) 268is obtained. In another location on the optimum adaptive torque controlblock diagram 242, permanent magnet flux Ψ_(m0) 270 is multiplied inmultiplier 272 with a value representing an amount of stator frequencyω_(e) 254 which, in terms of absolute value 256, exceeds rated statorfrequency ω_(e·rtd) by way of processing in block 258. As a result,multiplier 272 outputs a voltage Ψ_(m0)·ω_(e) 274. Rated voltage V_(rtd)276 may be divided by voltage Ψ_(m0)·ω_(e) 274 in division block 278 toproduce the normalized maximum available voltage {circumflex over(V)}_(max) 280. In another location on the optimum torque control blockdiagram 242, block 282 represents an equation that outputs motorinductance ratio K 284.

Normalized reference torque {circumflex over (T)}_(ref) 268, normalizedmaximum available voltage {circumflex over (V)}_(max) 280, and motorinductance ratio K 284 enter a three-dimensional table 286, whichrepresents a universal numerical solution to equation (43). For thegiven normalized reference torque {circumflex over (T)}_(ref) 268,normalized maximum available voltage {circumflex over (V)}_(max) 280,and motor inductance ratio K 284, the three-dimensional table 286 mayprovide an optimum normalized direct-axis current Î_(d·table) 288.

The optimum normalized direct-axis current Î_(d·table) 288 may besubsequently limited by a current limiter 290, which may limit theoptimum normalized direct-axis current Î_(d·table) 288 to a maximumnormalized stator current Î_(st·Max). The resulting current isrepresented by normalized direct-axis command current Î_(d·com) 292.Multiplying motor inductance ratio K 284 with the normalized commandcurrent Î_(d·com) 292 in multiplier 294 produces an interim currentvalue K·Î_(d) 296. Interim current value K·Î_(d) 296 and normalizedreference torque {circumflex over (T)}_(ref) 268 are employed byequation block 298 to determine a normalized quadrature-axis currentÎ_(q).

The normalized quadrature-axis current Î_(q) output by equation block298 and the normalized direct-axis command current Î_(d·com) 292 mayenter a current limiter 300, which subsequently may limit the normalizedquadrature-axis current Î_(q) to a value √{square root over(Î_(st·Max)−Î_(d·com) ²)}, which produces a normalized quadrature-axiscommand current Î_(q·com) 302. By multiplying the normalized direct-axiscommand current Î_(d·com) 292 and normalized quadrature-axis commandcurrent 302 by the contents of block 304,

$\frac{\Psi_{m\; 0}}{L_{d}},$

otherwise known as the characteristic current I_(df) a direct-axiscommand current in amperes I_(d·com) 306 and a quadrature-axis commandcurrent in amperes I_(q·com) 308 may be obtained. The direct-axiscommand current I_(d·com) 306 and the quadrature-axis command currentI_(q·com) 308 may subsequently be input in blocks 310 and 312,respectively, which represent the direct-axis and quadrature-axiscurrent loops, to obtain direct-axis command voltage V_(d·com) 314 andquadrature-axis command voltage V_(d·com) 316.

FIG. 6 depicts an exemplary two-dimensional component 318 of thethree-dimensional table 286. The two-dimensional component 318represents a table of numerical solutions for flux current 320,otherwise known as the normalized direct-axis current Î_(d) or theflux-producing current, at a single value D 322. Value D 322 is equal tothe normalized maximum available voltage {circumflex over (V)}_(max).

For varying values of torque per-unit 324, otherwise known as thenormalized reference torque {circumflex over (T)}_(ref), and values ofmotor inductance ratio K 326 ranging from zero to any appropriate valueat any appropriate intervals, various numerical solutions to equation(43) for flux current 320 are displayed. It should be appreciated thatany appropriate level of detail may be calculated and that the exemplarytwo-dimensional component of the three-dimensional table does notdisplay all the values that may be desired for the three-dimensionaltable 286.

Rather than implement a numerical solution, as described in FIGS. 5 and6, a closed loop solver solution may be derived based on equation (43).The closed-loop solver equation may be described as follows:

$\begin{matrix}{{\hat{V}}_{m\; {ax}}^{2} = {\frac{{\hat{T}}^{2} \cdot \left( {K + 1} \right)^{2}}{\left( {1 - {K \cdot {\hat{I}}_{d}}} \right)^{2}} + {\left( {1 + {\hat{I}}_{d}} \right)^{2}.}}} & (44)\end{matrix}$

FIG. 7 depicts an optimum torque control block diagram 328 based on theclosed loop solver equation (44) above. In a manner similar to that ofthe optimum torque control block diagram 242 of FIG. 5, the optimumtorque control block diagram 328 begins as a reference torque commandT_(ref) 330 enters a torque limiter 332, which limits the referencetorque command T_(ref) 330 to a torque limit T_(Lim) 334. It should benoted, however, the torque limiter 332 may also limit the referencetorque command T_(ref) 330 using the method illustrated by the torquelimit control block diagram 166 of FIG. 4.

To obtain torque limit T_(Lim) 334, a rated stator frequency ω_(e·rtd)336 is divided in division block 338 over a value representing an amountof stator frequency ω_(e) 340 which, in terms of absolute value 342,exceeds rated stator frequency ω_(e·rtd) by way of processing in block344. A frequency ratio ω_(ratio) 346 results, which may be understood torepresent a ratio of the rated stator frequency ω_(e·rtd) 336 to theamount of stator frequency ω_(e) 340 above base speed. The torque limitT_(Lim) 334 is obtained by multiplying a maximum torque limitT_(Lim·Max) 348 in multiplier 350 by frequency ratio ω_(ratio) 346.

By multiplying the output of torque limiter 332 with the contents ofblock 352, a normalized reference torque {circumflex over (T)}_(ref) 354may be obtained. The normalized reference torque {circumflex over(T)}_(ref) 354 will be employed elsewhere in the optimum torque controlblock diagram 328.

In another location on the optimum torque control block diagram 328,permanent magnet flux Ψ_(m0) 356 is multiplied in multiplier 358 with avalue representing stator frequency ω_(e) 360 which, in terms ofabsolute value 342, exceeds rated stator frequency ω_(e·rtd) by way ofprocessing in block 344. As a result, multiplier 358 outputs a voltageΨ_(m0)·ω_(e) 362. Rated voltage V_(rtd) 364 may be divided by voltageΨ_(m0)·ω_(e) 362 in division block 366, producing normalized maximumavailable voltage {circumflex over (V)}_(max).

When the output of division block 366, equal to normalized maximumavailable voltage {circumflex over (V)}_(max), is multiplied inmultiplier 368 against itself, the output is {circumflex over(V)}_(max·ref) ² 370. The value of {circumflex over (V)}_(max·ref) ² 370enters a summer 372, from which feedback {circumflex over (V)}_(max·fbk)374 is subtracted. The result enters a current controller 376, whichoutputs an optimum normalized direct-axis reference current Î_(d·ref)378. The optimum normalized direct-axis reference current Î_(d·ref) 378enters a summer 380 to which the contents of block 382, a value of 1,are added. The output of summer 380 is multiplied against itself inmultiplier 384, producing (1+Î_(d))² 386.

At another location on the optimum torque control block diagram 328,motor inductance ratio K 388 enters a summer 390 with the contents ofblock 382, a value of 1. The output of summer 390 is multiplied againstitself in multiplier 392, the result of which is subsequently multipliedin multiplier 394 with the a square of the normalized reference torque{circumflex over (T)}_(ref) 354, which results when the normalizedreference torque {circumflex over (T)}_(ref) 354 is multiplied againstitself in multiplier 396. The output of the multiplier 394 is{circumflex over (T)}²·(k+1)² 398.

Motor inductance ratio K 388 also enters multiplier 399 with the optimumnormalized direct-axis reference current Îd·ref 378, the output of whichis subtracted from the contents of block 400, a value of 1, in summer402. The output of summer 402 is subsequently multiplied against itselfin multiplier 404 to produce (1−K·Î_(d))² 406. The value {circumflexover (T)}²·(k+1)² 398 is divided by (1−K·Î_(d))² 406 in division block408, the result of which subsequently enters summer 410 with (1+Î_(d))386. Summer 410 ultimately outputs feedback {circumflex over(V)}_(max·fok) 374.

The optimum normalized direct-axis reference current Î_(d·ref) 378 alsoenters a current limiter 412, which may limit the optimum normalizeddirect-axis reference current Î_(d·ref) 378 to a maximum normalizedstator current Î_(st·Max). The resulting current is represented by anormalized direct-axis command current Î_(d·com) 414. Multiplying motorinductance ratio K 388 with the normalized command current Î_(d·com) 414in multiplier 416 produces an interim current value K·Î_(d) 418. Interimcurrent value K·Î_(d) 418 and normalized reference torque {circumflexover (T)}_(ref) 354 are subsequently employed by equation block 420 todetermine a normalized quadrature-axis current Î_(q·ref).

The normalized quadrature-axis current Î_(q·ref) output by equationblock 420 and the normalized direct-axis command current Î_(d·com) 414may enter a current limiter 422, which subsequently may limit thenormalized quadrature-axis current Î_(q·ref) to a value √{square rootover (Î_(st·Max) ²−Î_(d·com) ²)}, which produces a normalizedquadrature-axis command current Î_(q·com) 424.

By multiplying the normalized direct-axis command current Î_(d·com) 414by the contents of block 426,

$\frac{\Psi_{m\; 0}}{L_{d}},$

otherwise known as the characteristic current I_(df) a direct-axiscommand current in amperes I_(d·com) may be obtained. The direct-axiscommand current in amperes I_(d·com) 428 may subsequently be input inblock 430, which represents the direct-axis current loop, to obtain anoptimum direct-axis command voltage V_(d·com) 432. Similarly, bymultiplying the normalized quadrature-axis command current Î_(q·com) 424by the contents of block 426,

$\frac{\Psi_{m\; 0}}{L_{d}},$

otherwise known as the characteristic current I_(df), a quadrature-axiscommand current in amperes I_(q·com) 434 may be obtained. Thequadrature-axis command current I_(q·com) 434 may subsequently be inputin block 436, which represents the quadrature-axis current loop, toobtain an optimum quadrature-axis command voltage V_(q·com) 438.

It should be noted that the universal adaptive torque control algorithmspresented above may employ the universal torque limit approachesdescribed in FIG. 4. Additionally or alternatively, the universaladaptive torque control algorithms may employ other torque limitapproaches capable of limiting torque during field-weakening regionoperation.

While only certain features of the invention have been illustrated anddescribed herein, many modifications and changes will occur to thoseskilled in the art. It is, therefore, to be understood that the appendedclaims are intended to cover all such modifications and changes as fallwithin the true spirit of the invention.

1. A method for controlling a permanent magnet motor comprising:determining a normalized available voltage; determining a direct-axiscurrent based upon a reference torque command, the normalized availablevoltage, and an inductance ratio value of the motor; and outputting asignal for the determined direct-axis current to the motor.
 2. Themethod of claim 1, wherein determining the normalized available voltagecomprises dividing a rated voltage by a stator frequency multiplied anda rotor flux value.
 3. The method of claim 1, wherein the inductanceratio value of the motor is determined by dividing a value equal to aquadrature-axis inductance divided by a direct-axis inductance, and thensubtracting a value of 1 from the quotient.
 4. The method of claim 1,wherein the direct-axis current is a normalized direct-axis currentdetermined using a numerical method.
 5. The method of claim 1, whereinthe direct-axis current is determined via a precalculated table withsolutions based upon a plurality of normalized torque commands, aplurality of normalized available voltages, and the inductance ratiovalues of a plurality of different permanent magnet motors.
 6. Themethod of claim 5, wherein the precalculated table includes solutionsbased upon the following relationship between normalized direct-axiscurrent (Î_(d)), normalized reference torque commands ({circumflex over(T)}), normalized available voltages ({circumflex over (V)}_(max)), andinductance ratio values (K) of the motors:{circumflex over (T)} ²·(K+1)² ={circumflex over (V)} _(max) ²·(1−K·Î_(d))²−(1−K·Î _(d))²·(1+Î _(d))².
 7. The method of claim 1, whereindetermining the direct-axis current comprises determining a normalizeddirect-axis current using a closed-loop solver.
 8. The method of claim7, wherein the closed-loop solver is based upon the followingrelationship between the inductance ratio value (K) of the motor, thenormalized reference torque command ({circumflex over (T)}), and thenormalized available voltage ({circumflex over (V)}_(max)):${\hat{V}}_{m\; {ax}}^{2} = {\frac{{\hat{T}}^{2} \cdot \left( {K + 1} \right)^{2}}{\left( {1 - {K \cdot {\hat{I}}_{d}}} \right)^{2}} + {\left( {1 + {\hat{I}}_{d}} \right)^{2}.}}$9. A method for controlling a permanent magnet motor comprising:receiving a torque command; determining a stator frequency or speed; anddetermining a direct-axis current based on the torque command, thestator frequency or speed, a rated voltage of the motor, acharacteristic current of the motor, a rotor flux of the motor, and aninductance ratio value of the motor.
 10. The method of claim 9,comprising determining a normalized direct-axis current normalized tothe characteristic current of the motor, and wherein the direct-axiscurrent is determined by multiplying the normalized direct-axis currentby the characteristic current of the motor.
 11. The method of claim 9,wherein the inductance ratio value of the motor indicates that the motoris an interior permanent magnet motor.
 12. The method of claim 9,wherein the inductance ratio value of the motor indicates that the motoris a surface permanent magnet motor.
 13. A motor controller comprising:control circuitry configured to generate a control signal for driving athree phase inverter based at least in part on a value of a normalizeddirect-axis current, wherein the control circuitry is configured todetermine the value of the normalized direct-axis current based on anormalized torque command, a stator frequency, a rated voltage of themotor, a characteristic current of the motor, a rotor flux of the motor,and an inductance ratio value of the motor.
 14. The motor controller ofclaim 13, wherein the control circuitry is configured to determine thevalue of the normalized direct-axis current using a numerical method.15. The motor controller of claim 13, wherein the control circuitry isconfigured to determine the value the normalized direct-axis currentusing a using a precalculated table with solutions based upon aplurality of normalized torque commands, a plurality of normalizedavailable voltages, and inductance ratio values of a plurality ofdifferent permanent magnet motors.
 16. The motor controller of claim 15,wherein the precalculated table contains solutions to the followingrelationship between normalized direct-axis current (Î_(d)) normalizedtorque commands ({circumflex over (T)}), normalized available voltages({circumflex over (V)}_(max)), and inductance ratio values (K) of themotors:{circumflex over (T)} ²·(K+1)² ={circumflex over (V)} _(max) ²·(1−K·Î_(d))²−(1−K·Î _(d))²·(1+Î _(d))²,
 17. The motor controller of claim 13,wherein the control circuitry is configured to determine the value ofthe normalized direct-axis current using a closed-loop solver.
 18. Themotor controller of claims 17, wherein the closed-loop solver is basedupon the following relationship between the inductance ratio value ofthe motor (K), a normalized torque command ({circumflex over (T)}), anda normalized available voltage ({circumflex over (V)}_(max)):${{\hat{V}}_{m\; {ax}}^{2} = {\frac{{\hat{T}}^{2} \cdot \left( {K + 1} \right)^{2}}{\left( {1 - {K \cdot {\hat{I}}_{d}}} \right)^{2}} + \left( {1 + {\hat{I}}_{d}} \right)^{2}}},$19. A method of controlling a permanent magnet motor comprising:applying a flux-producing current to the motor configured to temporarilyweaken permanent magnets in the motor; applying a torque-producingcurrent to the permanent magnet motor; and varying the flux-producingcurrent and the torque-producing current based on normalized optimumcommand currents applicable to a plurality of permanent magnet motorswith known values of motor inductance ratio and characteristic current.20. The method of claim 19, wherein the normalized optimum commandcurrents are universal direct-axis currents normalized to a respectivecharacteristic current of each motor.
 21. The method of claim 20,wherein the universal direct-axis currents are determined based onnormalized torque command values, available voltage values, andinductance ratio values of the motors.
 22. The method of claim 21,wherein the universal direct-axis currents (Î_(d)) are determined usinga closed-loop solver in accordance with the following relationshipbetween inductance ratio values (K) of the motor, normalized torquecommand values ({circumflex over (T)}), and normalized available voltagevalues ({circumflex over (V)}_(max)):${\hat{V}}_{m\; {ax}}^{2} = {\frac{{\hat{T}}^{2} \cdot \left( {K + 1} \right)^{2}}{\left( {1 - {K \cdot {\hat{I}}_{d}}} \right)^{2}} + {\left( {1 + {\hat{I}}_{d}} \right)^{2}.}}$23. The method of claim 21, wherein the universal direct-axis currents(Î_(d)) are determined based on a three-dimensional table relatinginductance ratio values (K) of the motors, normalized torque commandvalues ({circumflex over (T)}), and normalized maximum available voltagevalues ({circumflex over (V)}_(max))according to the followingrelationship:{circumflex over (T)} ²·(K+1)² ={circumflex over (V)} _(max) ²·(1−K·Î_(d))²−(1−K·Î _(d))²·(1+Î _(d))².
 24. A computer memory device for usein controlling a permanent magnet motor in above base speed operationcomprising: a machine readable medium; and a lookup table encoded on themachine readable medium including a plurality of normalized values foroptimum direct-axis current, wherein each of the plurality of normalizedvalues for optimum direct-axis current corresponds respectively to avalue for optimum direct-axis current in a permanent magnet motor whenmultiplied by a characteristic current of the permanent magnet motor.25. The device of claim 23, wherein the plurality of normalized valuesfor optimum direct-axis current (Î_(d)) relates to an inductance ratiovalue (K) of the motor, a normalized torque command ({circumflex over(T)}), and a maximum available voltage ({circumflex over (V)}_(max))according to the following relationship:{circumflex over (T)} ²·(K+1)² ={circumflex over (V)} _(max) ²·(1−K·Î_(d))²−(1−K·Î _(d))²·(1+Î _(d))².